## FANDOM

10,845 Pages

Using Buchholz's psi notation, the ordinal $$\psi_0(\varepsilon_{\Omega_\omega + 1})$$, usually called the "Takeuti-Feferman-Buchholz ordinal", is a large countable ordinal that is the proof-theoretic ordinal of $$\Pi_1^1-\text{CA}+\text{BI}$$, a subsystem of second-order arithmetic.

It is the limit of Ferferman's theta notation, as well as the limit of Buchholz's psi notation.

It is also the ordinal measuring the strength of Buchholz hydras with $$\omega$$ labels, as well as the upper bound of the SCG function.

It was named by David Madore under the nickname "Gro-Tsen" on wikipedia[1].

## Sources Edit

1. https://en.wikipedia.org/w/index.php?title=Ordinal_collapsing_function&oldid=206127084 (see the end of "Going beyond the Bachmann-Howard ordinal")